A Stackelberg Game-Theoretic Framework with Q-Learning-Based Adaptive Thresholding for Mitigating Primary User Emulation Attacks in OFDM-Based Cognitive Radio Networks

Abstract

Primary User Emulation Attack (PUEA) is a critical denial-of-service threat in OFDM-based Cognitive Radio Networks (CRNs), in which an adversary mimics the signal characteristics of a licensed primary user (PU) to deny legitimate secondary users (SUs) access to idle spectrum. Conventional energy-detection sensing relies on a fixed decision threshold and is therefore structurally unable to adapt to a strategic, power-adjusting attacker. This paper develops a game-theoretic defense framework that models the interaction between the cognitive radio network (CRN) — acting as a Stackelberg leader that sets the spectrum-sensing threshold — and the PUEA attacker — acting as a follower that chooses its emulation transmit power. We show that the attacker's optimization is ill-posed under a detection-probability-only cost term, since attack success can be driven arbitrarily close to unity by unbounded transmit power, and we resolve this by introducing an exposure/power cost into the attacker's utility, yielding a well-defined best response. We derive, in closed form, the attacker's optimal emulation power as a function of the sensing threshold, and show that at the resulting equilibrium the attack success probability becomes invariant to the CRN's threshold choice for a fixed exposure cost — a structural property of the PUEA game that, to our knowledge, has not been reported in the existing literature. Building on this result and an augmented CRN utility that explicitly penalizes missed detection of the true PU, we derive a closed-form, Neyman–Pearson-type expression for the equilibrium sensing threshold. To relax the requirement that the CRN know the attacker's cost and channel parameters exactly, we embed the closed-form equilibrium as a warm start for a Q-learning agent that adaptively refines the threshold from observed sensing outcomes. We present the full mathematical derivation, an algorithmic realization of the combined Stackelberg–Q-learning scheme, a complexity and convergence discussion, and a numerical evaluation of the closed-form expressions across representative parameter ranges that confirms the predicted monotonic trends and reproduces classical asymptotic detection-theoretic behavior as a consistency check. Full OFDM physical-layer Monte Carlo and hardware testbed validation of the learning component are identified as the immediate next stage of this work. The proposed framework gives CRN operators a principled, adaptive alternative to fixed-threshold spectrum sensing under strategic PUEA.